This question was originally asked @ Related Post Plugin Support page: http://wordpress.org/support/topic/plugin-related-posts-thumbnails-wont-use-images-from-cdn-loads-local-files-only?replies=6#post-3749049
Basically, W3TC replaces all the images URLs to the CDN images URLs if it's enabled. This working fine if the images defined inside the CSS or inline img tag inside the pages/post/attachment etc..
However, the related post plugin prints the images as a background image inline into the post/pages, there we have a problem with W3TC URL replacement. W3TC wont replace the local URL with the remote CDN URL.
Any quick support will be appreciated!